I must have the same Thermos tumbler, and I've been wanting to do something about the rattle. The most annoying part is that the rear seat cupholders are much nicer, and would hold my tumbler perfectly, except I never sit in the rear.
I don't understand how this works, though. The tumbler is narrower than the cupholder. Don't you need something to pad the sides of the cupholder, rather than just the bottom?